Root-mean-square (RMS) is a fundamental measure of a signal's magnitude. The RMS value represents the amount of power the signal can deliver to particular load. Although numerous techniques have been devised for measuring the RMS value of a signal, the most practical and accurate solutions for electronic signal processing systems involve computational circuits that implement mathematically rigorous RMS functions. In these circuits, the input signal is squared and filtered to extract the root-mean value, and then an implicit or explicit square-root operation is performed to complete the RMS measurement.
FIG. 1 illustrates an example of a computational RMS-to-DC converter system. This system is embodied in commercial devices such as the AD536 and AD637 and described in the background of U.S. Pat. No. 6,429,720, which is by one of the same inventors of this patent disclosure and incorporated by reference. The dynamic range of the RMS subsystem is extended by arranging it in an automatic gain control (AGC) loop in which the RMS output signal VRMS is compared to a reference signal VREF by an operational amplifier 14. The resulting output signal VOUT is scaled and fed back to the gain control input VG of a variable gain amplifier (VGA) 13 which drives the input V1 of the RMS subsystem. These robust systems can be arranged to provide highly accurate RMS-to-DC conversion over a wide dynamic range, regardless of the input signal waveform, at frequencies up to several MHz.
Measuring the true RMS value of a higher frequency signal, however, is more difficult because the precision techniques utilized in the computational solutions described above have limited bandwidth. Thus, designers often resort to more rudimentary, but less accurate, circuits for measuring the RMS values of radio frequency (RF) signals. One such circuit is illustrated in FIG. 2 which shows a widely used diode detector for measuring the strength of an RF signal. The input is applied to diode D1 which charges capacitor C1 to almost the peak voltage of the RF signal. A termination resistor RTERM may be included at the input, and another resistor R1 is typically placed in parallel with C1 to set the time constant for the rate at which the capacitor voltage decays. Alternatively, a small pull-down current may be connected to the cathode of the diode for a similar reason.
The simplicity of this circuit allows it to operate at the highest frequencies that can be handled by the underlying semiconductor technology. Unfortunately, the accuracy of the output DCOUT is highly dependent on both the magnitude and the waveform of the input signal. At very low input signal levels, typically less than a few hundred millivolts, the circuit of FIG. 2 can actually provide a semblance of square-law or power response due to the relatively high curvature of the diode's logarithmic response at these voltage levels as shown in FIG. 3. This region of operation is sometimes referred to, imprecisely, as the “square law” or “RMS” region because the curvature of the response, influenced by the exponential diode characteristic, approximates a square law to a certain extent, and therefore, provides a modicum of RMS response.
At higher input levels, however, the circuit behaves as a peak detector (or envelope-following detector, depending on the value of R1) providing a linear measure of the peak or rectified average voltage of the RF input signal. Thus, the accuracy of the circuit of FIG. 2 is highly susceptible to variations in the input waveform. The output may be calibrated for a given waveform, e.g., a pure sinusoid, but then the circuit will only provide a relative measure of the amplitude of non-sinusoidal waveforms, rather than a true RMS value.
FIG. 4 illustrates another type of prior art detector known as a logarithmic amplifier (log amp). Log amps are widely used to convert signals having wide dynamic range into signals having smaller dynamic range. Such conversions are useful, for example, in wireless communication systems where a handset may receive a very strong RF signal when the user is close to a base station, but an extremely weak signal when the user moves away from the base station. The type of log amp illustrated in FIG. 4 is a demodulating progressive compression log amp which has a series of cascaded gain stages 10, and a series of rectifying detector cells 12, each cell being connected to a corresponding gain stage. The outputs of the detector cells are in current form, so they can be simply added and filtered to generate the log output signal.
Demodulating log amps can be used to provide a measure of the strength of wide-range RF signals. For example, the summed outputs from the transconductance detector cells 12 may be applied to a resistor which converts the current into a voltage VRSSI for use as a received signal strength indicator (RSSI). In wireless communications, the RSSI is indirectly used to control the power transmitted by the handset as well as the power transmitted by the base station for that channel.
The log amp illustrated in FIG. 4 can provide wide dynamic range and bandwidth, as well as high accuracy, through careful attention to implementation details. This wide dynamic range can be maintained even at high frequencies because the dynamic range is distributed over many stages, each having relatively low gain, to achieve the logarithmic function through the process of progressive compression.
Although a demodulating log amp as described above can provide a useful measure of the signal strength, it does not provide an accurate measure of the true power of the input signal. Instead, it only represents the amplitude of the fluctuating envelope of the RF input. Moreover, as with the diode detector of FIG. 2, the output of the log amp of FIG. 4 is highly dependent on the waveform of the input signal. However, in RF power measurement, it is the waveform of the envelope that may be variable.
This waveform dependency of diode detectors and log amps discussed above is less problematic in analog communication systems because the RF waveforms may be described as “well-behaved” and are nearly sinusoidal. However, the on-going transition to digital communication systems raises the need for data encoding techniques that frequently result in signals having complex waveforms and large crest factors, that is, the ratio of peak-to-RMS. These signals place greater demands on RMS detectors.
FIG. 5 illustrates a prior art system capable of measuring the true RMS values of RF signals having complex waveforms over wide dynamic ranges. The circuit of FIG. 5 includes a pair of squaring cells arranged to implement the “difference of squares” function, which is a mathematically accurate implementation of the RMS function. See, Barrie Gilbert: “Novel Technique For R.M.S.—D.C. Conversion Based On The Difference Of Squares,” Electronics Letters, 17 Apr. 1975, Vol. 11, No. 8, pp. 181-182, in which the error signal corresponding to IERR is generated by a single analog multiplier, generating (x−y)(x+y)=x2−y2.
The input signal SIN is applied to the first squaring cell 16 which generates a squared signal ISQR. A second input signal SREF is applied to the second squaring cell 18 which generates the squared signal IREF. A nulling circuit 19 generates VOUT in response to the integrated error between ISQR and IREF. The circuit of FIG. 5 can be configured for operation in a measurement mode, in which case VOUT is fed back to the second squaring cell as SREF. Alternatively, the system can be configured in a controller mode, in which case SOUT is used to control the gain of a device such as a power amplifier. In this mode, a sample of the output from the power amplifier is fed back to the first squaring cell as its input signal SIN, and a set-point target is applied to the second squaring cell as SREF. In all these modes, the feedback loop servos the system until the mean value of ISQR equals IREF.
If the squaring cells are implemented as simple transistor cells such as those disclosed in U.S. Pat. Nos. 6,204,719 and 6,172,549, which are by one of the same inventors as this patent disclosure and incorporated by reference, the system of FIG. 5 can provide a precise measure of the RMS value of RF signals for arbitrary waveforms. But even with this configuration, the accuracy deteriorates at very high operating frequencies, because the squaring cell 16 operates directly at the full RF frequency, and over the full dynamic range. Squaring cells, especially those based on transconductance (gm) cells, tend to have fairly small dynamic range because, at low input signal levels, their square-law behavior is very shallow and therefore lacks sensitivity, while at high input levels, the response curves progressively depart from a true square-law response.
To improve the dynamic range of the overall system, a variable gain amplifier (VGA) may be included at the input of the first squaring cell and arranged in an AGC feedback loop in a manner similar to that shown in the system of FIG. 5. In measurement mode, the output VOUT is also used as the gain control signal VG. A set-point voltage is applied to the second squaring cell as VREF. In this configuration, the circuit servos to maintain the RMS value at the input to the first squaring cell at the same value as VREF.
By setting VREF to a value that corresponds to a part of the squaring cell response curve having a large amount of curvature, the sensitivity to low input signals can be increased, and the dynamic range over which the first squaring cell must operate can be reduced. However, the squaring cell is still forced to operate over a large dynamic range. Moreover, the squaring function is inherently demanding because it doubles the dynamic range of the squared signal. That is, taking the square of a signal having a 40 dB range results in a squared signal having an 80 dB range. Maintaining this level of performance is extremely difficult at high operating frequencies.